Trigonometry Class

Question

A hamster running in a wheel of radius 15cm spins the wheel at 44 revolutions per minute

what is the angular speed of the wheel in radians/sec?

at what linear velocity is the hamster running in cm/sec?

Answer 1

There are 2π radians in 1 revolution so there are 44*2π radians/minute and since there is 1 minute in 60 seconds, the angular speed is 44*2π/60 radians/sec or approx 4.61 radians/sec.

Linear velocity = radius * angular speed = 15cm * 4.61 radians/sec = 69 cm/sec

Answer 2

Fun hamsters. The angular speed is 44 revolutions per minutes; however, we want it in rad/s so we convert.

ω=44rev/min(2π rad/rev)(1min/60sec)=44π/15 rad/s=9.22 rad/s

to get our linear velocity, relative to the wheel of the hamster, we have v=rω=0.15cm9.22rad/s

v=1.38m/s

Fast hamster.